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Conditional deep generative models as surrogates for spatial field solution reconstruction with quantified uncertainty in Structural Health Monitoring applications

Nicholas E. Silionis, Theodora Liangou, Konstantinos N. Anyfantis

TL;DR

The paper tackles the computational burden of Monte Carlo-based uncertainty quantification for high-dimensional structural responses in Structural Health Monitoring. It introduces a conditional deep generative surrogate based on a CNN-enhanced CVAE (CNN-CVAE) that learns the conditional distribution of spatial response fields given geometry parameters, enabling fast generation of calibrated samples with quantified uncertainty. Through two SHM-inspired case studies (a clamped plate and a ship-hull region), the authors demonstrate that the surrogate achieves accurate mean reconstructions and meaningful uncertainty representation while delivering substantial speedups, including online sampling times on the order of 0.19 s and significant offline cost reductions. The work highlights potential extensions to more expressive latent priors, sub-modeling applications, and time-dependent problems, underscoring its practical relevance for rapid, uncertainty-aware analysis in large-scale structural systems.

Abstract

In recent years, increasingly complex computational models are being built to describe physical systems which has led to increased use of surrogate models to reduce computational cost. In problems related to Structural Health Monitoring (SHM), models capable of both handling high-dimensional data and quantifying uncertainty are required. In this work, our goal is to propose a conditional deep generative model as a surrogate aimed at such applications and high-dimensional stochastic structural simulations in general. To that end, a conditional variational autoencoder (CVAE) utilizing convolutional neural networks (CNNs) is employed to obtain reconstructions of spatially ordered structural response quantities for structural elements that are subjected to stochastic loading. Two numerical examples, inspired by potential SHM applications, are utilized to demonstrate the performance of the surrogate. The model is able to achieve high reconstruction accuracy compared to the reference Finite Element (FE) solutions, while at the same time successfully encoding the load uncertainty.

Conditional deep generative models as surrogates for spatial field solution reconstruction with quantified uncertainty in Structural Health Monitoring applications

TL;DR

The paper tackles the computational burden of Monte Carlo-based uncertainty quantification for high-dimensional structural responses in Structural Health Monitoring. It introduces a conditional deep generative surrogate based on a CNN-enhanced CVAE (CNN-CVAE) that learns the conditional distribution of spatial response fields given geometry parameters, enabling fast generation of calibrated samples with quantified uncertainty. Through two SHM-inspired case studies (a clamped plate and a ship-hull region), the authors demonstrate that the surrogate achieves accurate mean reconstructions and meaningful uncertainty representation while delivering substantial speedups, including online sampling times on the order of 0.19 s and significant offline cost reductions. The work highlights potential extensions to more expressive latent priors, sub-modeling applications, and time-dependent problems, underscoring its practical relevance for rapid, uncertainty-aware analysis in large-scale structural systems.

Abstract

In recent years, increasingly complex computational models are being built to describe physical systems which has led to increased use of surrogate models to reduce computational cost. In problems related to Structural Health Monitoring (SHM), models capable of both handling high-dimensional data and quantifying uncertainty are required. In this work, our goal is to propose a conditional deep generative model as a surrogate aimed at such applications and high-dimensional stochastic structural simulations in general. To that end, a conditional variational autoencoder (CVAE) utilizing convolutional neural networks (CNNs) is employed to obtain reconstructions of spatially ordered structural response quantities for structural elements that are subjected to stochastic loading. Two numerical examples, inspired by potential SHM applications, are utilized to demonstrate the performance of the surrogate. The model is able to achieve high reconstruction accuracy compared to the reference Finite Element (FE) solutions, while at the same time successfully encoding the load uncertainty.
Paper Structure (9 sections, 23 equations, 14 figures, 2 tables)

This paper contains 9 sections, 23 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical background
  3. Autoencoders and deep neural networks
  4. Conditional variational autoencoders
  5. Conditional deep generative surrogate models for high-dimensional structural simulations
  6. Numerical examples
  7. Clamped plate subjected to stochastic lateral pressure
  8. Ship hull structural element under stochastic loading
  9. Concluding remarks

Figures (14)

  • Figure 1: Schematic representation of typical (a) autoencoder with one hidden layer, (b) artificial neuron and (c) 2D convolution kernel
  • Figure 2: Computational high-level architecture of (a) VAE and (b) CVAE during training and (c) CVAE inference process
  • Figure 3: Schematic representation of the offline (training) and online (inference) phases of the proposed CNN-CVAE surrogate model
  • Figure 4: Schematic representation of the clamped under stochastic pressure loading (a) and indicative realizations of the peak coordinates $(X_0, Y_0)$
  • Figure 5: Histogram of normalized error metrics for the mean (top row) and standard deviation (bottom row) for the clamped plate case where $t \sim \mathcal{U}[7, 10] \ \text{mm}$
  • ...and 9 more figures